Biologists rely on theories, apply models and construct explanations, but rarely reflect on their nature and structure. This book introduces key topics in philosophy of science to provide the required philosophical background for this kind of reflection, which is an important part of all aspects of research and communication in biology. It concisely and accessibly addresses fundamental questions such as: Why should biologists care about philosophy of science? How do concepts contribute to scientific advancement? What is the nature of scientific (...) controversies in the biological sciences? Chapters draw on contemporary examples and case studies from across biology, making the discussion relevant and insightful. Written for researchers and advanced undergraduate and graduate students across the life sciences, its aim is to encourage readers to become more philosophically minded and informed to enable better scientific practice. It is also an interesting and pertinent read for philosophers of science. (shrink)

ABSTRACT Modern elephant tusk is compared with Byzantine plaques as regards the surface microstructure by means of macrophotography. We are thus able to illustrate the differences between elephant bone and elephant tusk, whereas many exhibitions and publications wrongly refer to ivory as elephant bone. It is not uncommon in Greek and German literature to confuse elephant bone with elephant tusk. Bone is porous and white, whereas ivory is yellowish and compact with characteristic dentine structural lines. The structural lines of dentine (...) in plates made of organic mineralized tissues are diagnostic features of ivory that conclusively differentiate it from elephant bone. Dentine is also more compact than bone. Unlike bone, which is inexpensive and common, ivory is expensive and rare in keeping with the stature, wealth and power of Byzantine Emperors. (shrink)

Scientific knowledge is the most solid and robust kind of knowledge that humans have because of its inherent self-correcting character. Nevertheless, anti-evolutionists, climate denialists, and anti-vaxxers, among others, question some of the best-established scientific findings, making claims unsupported by empirical evidence. A common aspect of these claims is reference to the uncertainties of science concerning evolution, climate change, vaccination, and so on. This is inaccurate: whereas the broad picture is clear, there will always exist uncertainties about the details of the (...) respective phenomena. This book shows that uncertainty is an inherent feature of science that does not devalue it. In contrast, uncertainty advances science because it motivates further research. This is the first book on this topic that draws on philosophy of science to explain what uncertainty in science is and how it makes science advance. It contrasts evolution, climate change, and vaccination, where the uncertainties are exaggerated, and genetic testing and forensic science, where the uncertainties are usually overlooked. The goal is to discuss the scientific, psychological, and philosophical aspects of uncertainty in order to explain what it really is, what kinds of problems it actually poses, and why in the end it makes science advance. Contrary to public representations of scientific findings and conclusions that produce an intuitive but distorted view of science as certain, people need to understand and learn to live with uncertainty in science. This book is intended for anyone who wants to get a clear view of the nature of science. (shrink)

LetSbe the group of finitely supported permutations of a countably infinite set. Let$K[S]$be the group algebra ofSover a fieldKof characteristic 0. According to a theorem of Formanek and Lawrence,$K[S]$satisfies the ascending chain condition for two-sided ideals. We study the reverse mathematics of this theorem, proving its equivalence over$RC{A_0}$ to the statement that${\omega ^\omega }$is well ordered. Our equivalence proof proceeds via the statement that the Young diagrams form a well partial ordering.

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference. This paper examines in the (...) setting of categorial proof theory the conjecture that two derivations with the same premises and conclusions stand for the same proof if and only if they have the same generality. For that purpose generality is defined within a category whose arrows are equivalence relations on finite ordinals, where composition is rather complicated. Several examples are given of deductive systems of derivations covering fragments of logic, with the associated map into the category of equivalence relations of generality. This category is isomorphically represented in the category whose arrows are binary relations between finite ordinals, where composition is the usual simple composition of relations. This representation is related to a classical representation result of Richard Brauer. (shrink)

Current books on evolutionary theory all seem to take for granted the fact that students find evolution easy to understand when actually, from a psychological perspective, it is a rather counterintuitive idea. Evolutionary theory, like all scientific theories, is a means to understanding the natural world. Understanding Evolution is intended for undergraduate students in the life sciences, biology teachers or anyone wanting a basic introduction to evolutionary theory. Covering core concepts and the structure of evolutionary explanations, it clarifies both what (...) evolution is about and why so many people find it difficult to grasp. The book provides an introduction to the major concepts and conceptual obstacles to understanding evolution, including the development of Darwin's theory, and a detailed presentation of the most important evolutionary concepts. Bridging the gap between the concepts and conceptual obstacles, Understanding Evolution presents evolutionary theory with a clarity and vision students will quickly appreciate. (shrink)

In standard model theory, deductions are not the things one models. But in general proof theory, in particular in categorial proof theory, one finds models of deductions, and the purpose here is to motivate a simple example of such models. This will be a model of deductions performed within an abstract context, where we do not have any particular logical constant, but something underlying all logical constants. In this context, deductions are represented by arrows in categories involved in a general (...) adjoint situation. To motivate the notion of adjointness, one of the central notions of category theory, and of mathematics in general, it is first considered how some features of it occur in set-theoretical axioms and in the axioms of the lambda calculus. Next, it is explained how this notion arises in the context of deduction, where it characterizes logical constants. It is shown also how the categorial point of view suggests an analysis of propositional identity. The problem of propositional identity, i.e., the problem of identity of meaning for propositions, is no doubt a philosophical problem, but the spirit of the analysis proposed here will be rather mathematical. Finally, it is considered whether models of deductions can pretend to be a semantics. This question, which as so many questions having to do with meaning brings us to that wall that blocked linguists and philosophers during the whole of the twentieth century, is merely posed. At the very end, there is the example of a geometrical model of adjunction. Without pretending that it is a semantics, it is hoped that this model may prove illuminating and useful. (shrink)

Textbook descriptions of the foundations of Genetics give the impression that besides Mendel’s no other research on heredity took place during the nineteenth century. However, the publication of the Origin of Species in 1859, and the criticism that it received, placed the study of heredity at the centre of biological thought. Consequently, Herbert Spencer, Charles Darwin himself, Francis Galton, William Keith Brooks, Carl von Nägeli, August Weismann, and Hugo de Vries attempted to develop theories of heredity under an evolutionary perspective, (...) and they were all influenced by each other in various ways. Nonetheless, only Nägeli became aware of Mendel’s experimental work; it has also been questioned whether Mendel even had the intention to develop a theory of heredity. In this article, a short presentation of these theories is made, based on the original writings. The major aim of this article is to suggest that Mendel was definitely not the only one studying heredity before 1900, if he even did this, as may be inferred by textbooks. Although his work had a major impact after 1900, it had no impact during the latter half of the nineteenth century when an active community of students of heredity emerged. Thus, textbooks should not only present the work of Mendel, but also provide a wider view of the actual history and a depiction of science as a social process. (shrink)

Though the ancient Greek philosophical concept of scholê is usually translated as 'leisure', there is a vast difference between the two. Leisure, derived from Latin licere, has its roots in Roman otium and connotes the uses of free time in ways permitted by the status quo. Scholê is the actualization of mind and one's humanity within a republic that devotes its culture to making such a choice possible. This volume traces the background in Greek culture and the writings of Plato (...) of a daring proposal presented by Aristotle, that scholê is a principle for political organization. The concept of scholê by and large did not survive Aristotle. To sharpen our understanding of scholê the book goes on to identify the concepts of leisure which we have inherited from the intellectuals of the Hellenistic and Roman empires and the early Church Fathers. Scholê also had its contrary ascholia – busyness – which Plato described as a social and psychological pathology and his analysis suggests why, due to these ills, current visions of a leisure society are highly unlikely. (shrink)

Les absents jouent un rôle considérable dans la création des signes qui servent, dans toute société, à désigner, nommer, et même instituer les places des présents et celles des absents tout en mettant du sens dans leurs relations. La sémiotique conçoit ainsi le processus d'humanisation à travers la création des signes alors que la psychanalyse a permis, à sa manière, de voir combien le monde des absents participe à la construction psychique du sujet. La fonction de l'absence perceptive chez le (...) bébé est également étudiée dans cet ouvrage dans sa contribution à la transformation des signes gestuels binaires en signes ternaires qui intègrent du sens. Ces transformations sémiotiques sont aussi éclairées par le regard des poètes et des philosophes présents dans cet ouvrage. (shrink)

Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the same generality if after generalizing maximally (...) the rules involved in them they yield the same premises and conclusions up to a renaming of variables. These two proposals proved to be extensionally equivalent only for limited fragments of logic. The normalization proposal stands behind very successful applications of the typed lambda calculus and of category theory in the proof theory of intuitionistic logic. In classical logic, however, it did not fare well. The generality proposal was rather neglected in logic, though related matters were much studied in pure category theory in connection with coherence problems, and there are also links to low-dimensional topology and linear algebra. This proposal seems more promising than the other one for the general proof theory of classical logic. (shrink)

This paper presents an emerging aspect of intentionality through recent Artificial Intelligence (AI) developments in art and design. Our main thesis is that, if we focus just on the outcome of the artistic process, the intentionality of the artist does not have any relevance. Intention is measured as a result of actions regardless of whether they are human-based or not as long as there is an esthetical value intersubjectively acknowledged. In other words, what matters is the ‘intentio’ embedded in the (...) work of art (the output) rather than the ‘intendere’ (the process). By considering the former aspect, intentionality becomes free of human intervention, therefore 'unintentional'. This thesis is supported through a range of examples related to AI in general and AI art in particular. However, in the case of a self-driving vehicle, the macro-goal of the system is fixed by humans, even though the AI system itself will take care of decomposing the macro-goal into a set of micro-goals and take the corresponding decisions. In the case of art, the system does not need to have any exterior goal to the extent that art is pure freedom of expression, as many philosophers have acknowledged. In this sense, the decisions of any AI system generating art or design are independent of humans and must be judged only on the ground of the final outcome. A work of art will be judged ‘artistic’ to the extent that humans will recognize an artistic intent in the work itself. In particular, the introduction of random processes makes an AI-generated artwork fully independent of human creativity. (shrink)

The purpose of this paper is to connect the proof theory and the model theory of a family of propositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related toBCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the structural (...) rules. Next, Hubert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.The first part of the paper, which follows, contains the first two sections, which deal with sequent-systems and Hubert-formulations. The second part, due to appear in the next issue of this journal, will contain the third section, which deals with groupoid models. (shrink)

Science appeared in modern Greece in the first decades after its establishment as a sovereign state in 1828. The University of Athens, the Royal Observatory, the Botanical Garden, and the Natural History Museum were quickly established as spaces of scientific activity. Greek scientists were enthusiastic participants in the emerging Greek public sphere, often not only as science experts, but also as poets, intellectuals and political personae. In a space whose cultural, intellectual and historical boundaries were still being negotiated, the choice (...) of language was not a given but a pressing, sensitive national desideratum. This article examines how Greek scientists used languages to communicate with their peers and with their publics, how they handled terminology and nomenclature, and how the issues surrounding the Greek language in particular affected their practice as scientists. The article aims to show that, in nineteenth-century Greece, languages were not passive, neutral vehicles of communication, but rather integral components of the practice of science. (shrink)

This book presents analyses of philosophical topics of importance to biology education. It is intended foremost for biology educators and teachers, and aims to show how philosophy of science in general, and philosophy of biology in particular, ...

The purpose of this work is to present Gentzen-style formulations of S5 and S4 based on sequents of higher levels. Sequents of level 1 are like ordinary sequents, sequents of level 1 have collections of sequents of level 1 on the left and right of the turnstile, etc. Rules for modal constants involve sequents of level 2, whereas rules for customary logical constants of first-order logic with identity involve only sequents of level 1. A restriction on Thinning on the right (...) of level 2, which when applied to Thinning on the right of level 1 produces intuitionistic out of classical logic (without changing anything else), produces S4 out of S5 (without changing anything else). This characterization of modal constants with sequents of level 2 is unique in the following sense. If constants which differ only graphically are given a formally identical characterization, they can be shown inter-replaceable (not only uniformly) with the original constants salva provability. Customary characterizations of modal constants with sequents of level 1, as well as characterizations in Hilbert-style axiomatizations, are not unique in this sense. This parallels the case with implication, which is not uniquely characterized in Hilbert-style axiomatizations, but can be uniquely characterized with sequents of level 1. These results bear upon theories of philosophical logic which attempt to characterize logical constants syntactically. They also provide an illustration of how alternative logics differ only in their structural rules, whereas their rules for logical constants are identical. (shrink)

This is a review, with historical and critical comments, of a paper by I. E. Orlov from 1928, which gives the oldest known axiomatization of the implication-negation fragment of the relevant logic R. Orlov's paper also foreshadows the modal translation of systems with an intuitionistic negation into S4-type extensions of systems with a classical, involutive, negation. Orlov introduces the modal postulates of S4 before Becker, Lewis and Gödel. Orlov's work, which seems to be nearly completely ignored, is related to the (...) contemporaneous work on the axiomatization of intuitionistic logic. (shrink)

Models for the Lambek calculus of syntactic categories surveyed here are based on frames that are in principle of the same type as Kripke frames for intuitionistic logic. These models are extracted from the literature on models for relevant logics, in particular the ternary relationed models introduced in the early seventies. The purpose of this brief survey is to locate some open completeness problems for variants of the Lambek calculus in the context of completeness results based on various types of (...) ternary relational models. (shrink)

This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of (...) formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated. (shrink)

The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of ‘absolute space’. When applied to classical mechanics, under the guise of an extended symmetry group, this procedure is known to lead to an equation of motion with inertial-like forces that are sourced by the mass distribution of the system itself. In this paper we follow a similar procedure and reformulate the Schrödinger equation of non-relativistic quantum mechanics (...) in a fully Machian way. Just like its classical counterpart, the resulting quantum theory is fully relational in the positions and momenta of the bodies comprising a given physical system, leaving no room for the notion of absolute space. (shrink)

This paper presents duality results between categories of neighbourhood frames for modal logic and categories of modal algebras (i.e. Boolean algebras with an additional unary operation). These results extend results of Goldblatt and Thomason about categories of relational frames for modal logic.

What are genes? What do genes do? These seemingly simple questions are in fact challenging to answer accurately. As a result, there are widespread misunderstandings and over-simplistic answers, which lead to common conceptions widely portrayed in the media, such as the existence of a gene 'for' a particular characteristic or disease. In reality, the DNA we inherit interacts continuously with the environment and functions differently as we age. What our parents hand down to us is just the beginning of our (...) life story. This comprehensive book analyses and explains the gene concept, combining philosophical, historical, psychological and educational perspectives with current research in genetics and genomics. It summarises what we currently know and do not know about genes and the potential impact of genetics on all our lives. Making Sense of Genes is an accessible but rigorous introduction to contemporary genetics concepts for non-experts, undergraduate students, teachers and healthcare professionals. (shrink)

Although macroevolution has been the subject of sustained attention in the history and philosophy of science (HPS) community, only in recent years have science educators begun to more fully engage with the topic. This chapter first explores how science educators have conceptualized macroevolution and how their perspectives align with the views from HPS. Second, it illustrates how science educators’ limited engagement with HPS scholarship on macroevolution has influenced construct delineation, measurement instrument development, and educational arguments about which aspects of macroevolution (...) are most important for students to learn. Third, it discusses how scientific debates about the causal factors responsible for macroevolutionary patterns have been exploited by creationists and have impacted the teaching of evolution. Finally, it emphasizes that the rich perspectives that HPS has to offer on the important topic of macroevolution have yet to be integrated into science education scholarship. (shrink)

In Neither Physics Nor Chemistry, Kostas Gavroglu and Ana Simoes examine the evolution of quantum chemistry into an autonomous discipline, tracing its development from the publication of early papers in the 1920s to the dramatic changes ...

Explores Aristotle's theory of the causes that give rise to stasis ('civic disorder'), and provides an original and systematic account of his understanding of political justice and friendship.

This paper analyzes the ongoing university reform in Russia by underlining historical roots and peculiarities of its system of higher education. It is pointed out that the Soviet model of economy, political and ideological bias deeply impacted the university system and enforced its estrangement from foreign universities. A limited number of the best Soviet higher education institutions which provided a military-oriented education and fundamental research were re-casted along the so called “PhysTech” system after the end of the WWII. As a (...) result of this system, higher education and R&D in Russia is not presently competitive in the educational international market. Closing the gap between Russian universities and the “global university” approach and raising university competitiveness are the main objectives of the current reform in science and education. As universities are considered core actors of knowledge economy, a new set of federal and national research universities was created. However, reform faces numerous conceptual and institutional obstacles, risks and constraints are significant, and positive outcomes elusive. (shrink)

What was science for the Orthodox Greek theologian of the nineteenth century? How did it feature in his (theologians were all men at the time) own work? This article is an attempt to describe the science and religion interactions by placing Greek Orthodox theologians of the nineteenth century in the center of the historical narrative, rather than treat them as occasional deuteragonists in the scientists’ historiography. The picture that emerges is far more complicated than one of antagonism, indifference, conflict, or (...) coexistence. Greek theologians saw themselves as scientists and treated theology as a positive, rational science. They developed strategies to delineate their disciplinary borders and safeguard their identity as expert scholars by harnessing their university and academic credentials. For that reason, they had to invoke famous German and other Western theologians, while ensuring that they were seen as true defenders of Orthodox Christianity. The idea of science was an integral part of this achievement. (shrink)

Who should rule? -- The exercise of power : liberty -- Politics as activity : participation, deliberation, conflict -- The end of politics : the good life, a better world.

The purpose of this paper is to connect the proof theory and the model theory of a family of prepositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related to BCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the (...) structural rules. Next, Hilbert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.Below is the sequel to the first part of the paper, which appeared in the previous issue of this journal (vol. 47 (1988), pp. 353–386). The first part contained sections on sequent-systems and Hilbert-formulations, and here is the third section on groupoid models. This second part is meant to be read in conjunction with the first part. (shrink)

Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic. It is proved that first-order variants of these logics with an intuitionistic negation can be embedded by modal translations into S4-type extensions of these logics with a classical, involutive, negation. Related embeddings via translations like the double-negation translation are also considered. Embeddings into analogues of S4 are obtained with (...) the help of cut elimination for sequent formulations of our substructural logics and their modal extensions. These results are proved for systems with equality too. (shrink)